Incompleteness in the Land of Sets
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The Hilbert II links page has plenty more links to relevant sites.
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In this book Torkel Franzen examines various ways that this theorem has been wrongly quoted, and tries to set the reader straight on what it is really about. He looks at what has been said about incompleteness in physics, in theology and of course in various postmodern ramblings.
Reviews of Godel's theorem : an incomplete guide to its use and abuse Buy this book Amazon. In this book he gives an account of some of his work.
Incompleteness Land Sets by Melvin Fitting
Reviews of Meta Math! Russell's paradox arises when we consider those sets that do not belong to themselves. The collection of such sets cannot constitute a set. Step back a bit.
Logical formulas define sets in a standard model. Formulas, being mathematical objects, can be thought of as sets themselves-mathematics reduces to set theory. Consider those formulas that do not belong to the set they define.
The collection of such formulas is not definable by a formula, by the same argument that Russell used.